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From "Martin Desruisseaux (JIRA)" <j...@apache.org>
Subject [jira] [Created] (SIS-155) Area calculation on ellipsoid
Date Wed, 18 Dec 2013 17:20:06 GMT
```Martin Desruisseaux created SIS-155:
---------------------------------------

Summary: Area calculation on ellipsoid
Key: SIS-155
URL: https://issues.apache.org/jira/browse/SIS-155
Project: Spatial Information Systems
Issue Type: New Feature
Components: Referencing
Affects Versions: 0.3
Reporter: Martin Desruisseaux

We need a method for calculating the area inside a polygon on the ellipsoid. An algorithm
working in Cartesian coordinate system is available there:

* http://www.mathopenref.com/coordpolygonarea2.html

This algorithm can be adapted to spherical coordinate systems by replacing the area sum by
(note that this replacement uses vertical strips instead than horizontal ones):

{code:java}
s += (λ2 - λ1) * (2 + sin(φ1) + sin(φ2));
{code}

{code:java}
area = abs(s * r² / 2);
{code}

The _r_ value could be approximated to the authalic radius (the radius of a hypothetical sphere
having the same surface than the ellipsoid). However an article on http://www.geodyssey.com/papers/ggelare.html
seems to use a more local approximation, where _a_ and _b_ are semi-major and semi-minor axis
lengths:

{code:java}
s = sin(φ)
c = cos(φ)
r = (a²b) / (a²c² + b²s²)
{code}

This task just write down some ideas. We probably need to read the above-cited article and
other internet resources more carefully.

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